Hysteresis losses of fine filamentary superconductors including field dependent critical current density

Using the force versus displacement curve for the flux lines, the hysteresis losses of thin superconducting slabs in transverse magnetic field were calculated. Especially, Kim's model for the field dependence of the critical current densityJ_c 1/(B_m+B_o) was used (B_m- the applied field,B_o = const.). The results are compared with the corresponding model usingJ_c = const., as well as with the critical state model without the force versus displacement curve. It is shown that the losses per volume are always decreasing with decreasing slab thickness. In the case of large background fieldB₀ and small amplitude of the ripple fieldb₀, the corrections are small with respect to the caseJ_c= const. Without background field, the hysteresis losses are somewhat larger than for field independentJ_c. Therefore, in accordance with our previous paper, the strong decrease of hysteresis losses with decreasing filament diameter in lower magnetic fields cannot be explained by the reversible motion of flux lines in the superconductors. It is suggested that this strong decrease is connected with the reversible motion of flux not connected with flux lines in superconductors, the diameter of which is comparable with the London penetration depth .